### Problem Statement (9.31 and 9.32)Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x-axis.### Diagram DescriptionThe diagram is labeled as Fig. P9.32. It features a composite shape on a coordinate plane with x and y axes. The structure consists of a large rectangle with two smaller rectangles subtracted from its interior, forming a C-shaped area. #### Dimensions:- The exterior rectangle's total width is 8 inches (composed of two 3-inch segments and two 2-inch segments).- The exterior rectangle's total height is 4 inches (two segments of 2 inches each).- The smaller rectangle on the left has dimensions of 6 inches by 2 inches.- The smaller rectangle on the right has dimensions of 4 inches by 2 inches.- The shaded area's top is positioned at y = 2 inches and its bottom is at y = -2 inches.- The right edge of both inner rectangles aligns with x = 2 inches.The point \(O\) marks the origin at the center of the structure, aligned with the x and y axes.### Task- Calculate the moment of inertia for the shaded area concerning the x-axis.- Calculate the radius of gyration for the shaded area concerning the x-axis.

The schematic diagram of the area is shown below:

9.31 and 9.32 Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis. 2 in. 2 in. 3 in. 3 in.- 1 in. 3 in. 2 in. 2 in. 3 in. 1 in. 1 in. -1 in. Fig. P9.32.

9.31 and 9.32 Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x axis. 2 in. 2 in. 3 in. 3 in.- 1 in. 3 in. 2 in. 2 in. 3 in. 1 in. 1 in. -1 in. Fig. P9.32.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

### Problem Statement (9.31 and 9.32)

Determine the moment of inertia and the radius of gyration of the shaded area with respect to the x-axis.

### Diagram Description

The diagram is labeled as Fig. P9.32. It features a composite shape on a coordinate plane with x and y axes. The structure consists of a large rectangle with two smaller rectangles subtracted from its interior, forming a C-shaped area.

#### Dimensions:
- The exterior rectangle's total width is 8 inches (composed of two 3-inch segments and two 2-inch segments).
- The exterior rectangle's total height is 4 inches (two segments of 2 inches each).
- The smaller rectangle on the left has dimensions of 6 inches by 2 inches.
- The smaller rectangle on the right has dimensions of 4 inches by 2 inches.
- The shaded area's top is positioned at y = 2 inches and its bottom is at y = -2 inches.
- The right edge of both inner rectangles aligns with x = 2 inches.

The point \(O\) marks the origin at the center of the structure, aligned with the x and y axes.

### Task

- Calculate the moment of inertia for the shaded area concerning the x-axis.
- Calculate the radius of gyration for the shaded area concerning the x-axis.

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